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Inviscid Mechanism for Unsteady Waves Fig of c I vs kz shows as c i  0 out-of-phase perturbation to \Delta u becomes very large. Occurs in very thin layer of thickness of O(c_i). Vorticity ( ω y) amplifies on lee-side and reduced on upwind-side. Leads to mean stream lines being deflected, "lower pressure" on the lee side  "higher drag". when c i > 0, wave grows; c i <0 wave decays. But there is a net force on the wave produced by the integrated effect of the critical layer as |ci|->0. ( Miles did not calculate profiles-only the integral effect prop to U’’(at z=zc))

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Conclusions Physical growth mechanism is NOT soley due to steady Critical layer CL. Critical layer is unsteady problem. Growing/decaying wave amplitude in the groups increases CL on the downside of group where wave shape changes. CL plays an important role on sheltering. Asymmetrical sheltering leads to reduction in wind speed.

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2. Tsunami waves The problem of negative tsunami waves travelling over long distances, being transformed into positive waves and impacting on beaches, before or after the transition. Ref.Klettner, C.A., Balasubramanian, S., Hunt, J.C.R., Fernando, H.J.S., Voropayev, S.I. and Eames, I., 2012 Draw down and run-up of tsunami waves on sloping beaches. Proc. Inst. Civil Engineers-Engineering and Computational Mechanics 165,119-129.

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Negative tsunami on a beach,tested in ASU hyd. lab Note the sharp rise on the downstream end behind the deepening depression-same n-l process as for + waves. Depression leads to shore line retreat  large wave up the beach.

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Note warming and less ice in Arctic ocean affects Wind driven Waves, which break up ice and leads to Further warming (Wadhams), and Less ice, plus seismic activity, is likely to Lead to tsunamis on very flat arctic coastline Concetn to local communities and to extractive industries And to possible transport dangers -